<u><em>Answer:</em></u>
A. (3x²-4x-5)(2x⁶-5)
<u><em>Explanation:</em></u>
<u>The fundamental theorem of Algebra states that:</u>
"A polynomial of degree 'n' will have exactly 'n' number of roots"
We know that the degree of the polynomial is given by the highest power of the polynomial.
Applying the above theorem on the given question, we can deduce that the polynomial that has exactly 8 roots is the polynomial of the 8th degree
<u>Now, let's check the choices:</u>
<u>A. (3x²-4x-5)(2x⁶-5)</u>
The term with the highest power will be (3x²)(2x⁶) = 6x⁸
Therefore, the polynomial is of 8th degree which means it has exactly 8 roots. This option is correct.
<u>B. (3x⁴+2x)⁴</u>
The term with the highest power will be (3x⁴)⁴ = 81x¹⁶
Therefore, the polynomial is of 16th degree which means it has exactly 16 roots. This option is incorrect.
<u>C. (4x²-7)³</u>
The term with the highest power will be (4x²)³ = 64x⁶
Therefore, the polynomial is of 6th degree which means that it has exactly 6 roots. This option is incorrect
<u>D. (6x⁸-4x⁵-1)(3x²-4)</u>
The term with the highest power will be (6x⁸)(3x²) = 18x¹⁰
Therefore, the polynomial is of 10th degree which means that it has exactly 10 roots. This option is incorrect
Hope this helps :)
Answer : (13)
Let x be the number of party favors in each (27 boxes)
Let y be the number of favors in last box
Given : total of party favors = 1552
27 boxes + last box = 1552
27x + y = 1552
We divide 1552 by 27, the quotient will be our x and the remainder will be y(number of party favors in last box)
Use long division
= 57 and remainder is 13
the number of party favors in each of (27 boxes) = 57
the number of party favors in last box = 13
So, there are 13 party favors in last box.
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Answer:
See below
Step-by-step explanation:
Remember, we have two quantifiers, the existential quantifier ∃, and the universal quantifier ∀. The existential ∃ translates to English as "for some" or "there exists", whereas ∀ means "for all" or "every". We will also use the negation operator ¬.
First, let's write the proposition using quantifiers. "There is someone in this class who does not have a good attitude" translates to "(∃x)(¬S(x))". ∃x means that there exists a person in this class x. ¬S(x) means that x, the person that exists because of the quantifier, does not have a good attitude.
The negation is "¬(∃x)(¬S(x))" or equivalently "(∀x)(S(x))". To negate a proposition using quantifiers, change the quantifier (existential to universal and viceversa) and negate the predicate (in this case we negated ¬S(x)).
In English, "(∀x)(S(x))" means "Every person in this class has a good attitude".
If you complete the square you get
and as any number squared is positive and 4 is positive, the result must be positive
